Stress & Strain Calculator
Find stress, strain, or modulus of elasticity.
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Formulas
σ = F / AStress in Pascals (N/m²) or MPa
E = σ / εYoung's Modulus (elastic modulus)
Stress & Strain
Stress = force per area. Strain = relative deformation. Young's Modulus: Steel ~200 GPa, Aluminum ~69 GPa, Copper ~117 GPa, Wood ~11 GPa.
Understanding Stress and Strain
Stress measures the internal force a material carries per unit of cross-sectional area when a load is applied. It is the starting point for nearly all structural and mechanical design:
σ = F / Aσ (sigma) is stress in pascals, F is the applied force in newtons, and A is the cross-sectional area in square metres.
Strain is the related deformation — the fractional change in length under load (ε = ΔL/L). Within the elastic region, stress and strain are linked by the material's modulus of elasticity (σ = Eε).
Worked Example
A 10 kN load on a rod with 100 mm² (1×10⁻⁴ m²) cross-section:
σ = 10000 / 0.0001 = 100×10⁶ Pa = 100 MPa
For structural steel with a yield strength around 250 MPa, this rod is working well within its elastic limit.
Key Points on the Stress-Strain Curve
| Point | Meaning |
|---|---|
| Proportional limit | Stress and strain stay linear |
| Yield strength | Permanent deformation begins |
| Ultimate strength | Maximum stress the material bears |
| Fracture point | Material breaks |
Engineers design components to stay below the yield strength, applying a factor of safety to account for uncertainty.
Frequently Asked Questions
What is the difference between stress and pressure?
Both are force per area, but pressure acts externally on a surface from a fluid, while stress is the internal force distribution within a solid material resisting a load.
What is a factor of safety?
The ratio of a material's strength to the actual working stress. A factor of 2 means the part can carry twice its expected load before yielding.
Is this tensile or compressive stress?
The formula σ = F/A applies to both. The sign and the material's behaviour differ: many materials are much stronger in compression than tension, or vice versa.